With the K-Means algorithm, each object is assigned to exactly one cluster. It is assigned to this cluster with a probability equal to 1.0. It is assigned to all other clusters with a probability equal to 0.0. This is hard clustering.
Instead of distance, you can use a probabilistic measure to determine cluster membership. For example, you can ...

Hierarchical clustering could be very useful because it is easy to see the optimal number of clusters in a dendrogram and because the dendrogram visualizes the clusters and the process of building of that clusters. However, hierarchical methods don’t scale well. Just imagine how cluttered a dendrogram would be if 10,000 cases would be shown on ...